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Mat. Sb., 2014, Volume 205, Number 9, Pages 49–64 (Mi msb8361)  

This article is cited in 4 scientific papers (total in 4 papers)

The topology of integrable systems with incomplete fields

K. R. Aleshkin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Liouville's theorem holds for Hamiltonian systems with complete Hamiltonian fields which possess a complete involutive system of first integrals; such systems are called Liouville-integrable. In this paper integrable systems with incomplete Hamiltonian fields are investigated. It is shown that Liouville's theorem remains valid in the case of a single incomplete field, while if the number of incomplete fields is greater, a certain analogue of the theorem holds. An integrable system on the algebra $\mathfrak{sl}(3)$ is taken as an example.
Bibliography: 11 titles.

Keywords: integrable systems, incomplete fields, Liouville's theorem, Lie algebras.

DOI: https://doi.org/10.4213/sm8361

Full text: PDF file (500 kB)
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English version:
Sbornik: Mathematics, 2014, 205:9, 1264–1278

Bibliographic databases:

UDC: 517.938.5+514.763.2
MSC: 37C10, 37J35
Received: 17.03.2014

Citation: K. R. Aleshkin, “The topology of integrable systems with incomplete fields”, Mat. Sb., 205:9 (2014), 49–64; Sb. Math., 205:9 (2014), 1264–1278

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8361
  • http://mi.mathnet.ru/eng/msb/v205/i9/p49

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. A. Zagryadskii, “Bertranovskie sistemy i ikh fazovoe prostranstvo”, Nauka i obrazovanie: nauchnoe izdanie MGTU im. N.E. Baumana, 2014, no. 12, 365–386  elib
    2. K. Aleshkin, A. Izostmov, “Euler equations on the general linear group, cubic curves, and inscribed hexagons”, Enseign. Math., 62:1-2 (2016), 143–170  crossref  mathscinet  zmath  isi
    3. D. A. Fedoseev, A. T. Fomenko, “Nekompaktnye osobennosti integriruemykh dinamicheskikh sistem”, Fundament. i prikl. matem., 21:6 (2016), 217–243  mathnet
    4. S. S. Nikolaenko, “Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds”, Sb. Math., 211:8 (2020), 1127–1158  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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